Fig. REF  presents the required number of decoding time-steps for the proposed successive syndrome-check decoder that is based on SC decoding for \(\mathcal {P}(128,64)\)  used in the 5G standard. The results are compared with three fast SC decoders in the literature [1]}, [2]}, [3]}. Fig. REF  shows the latency results of the proposed successive syndrome-check decoder based on SCL decoding for \(\mathcal {P}(128,64)\)  used in the 5G standard. The results are compared with three fast SCL decoders in [4]}, [5]}, [6]} and for all the decoders, \(L=8\) . Fig. REF  plots the number of time-steps required for the proposed decoders and the fast SCL decoders in [4]}, [5]}, [6]} to decode a Reed-Muller (RM) code of length 128 and rate \(\frac{1}{2}\) . The list size is set to \(L=32\)  to provide a frame error rate (FER) close to the maximum-likelihood decoding performance. It can be seen that in all the considered cases, the proposed method requires a smaller number of decoding time-steps in comparison with all the considered fast SC and SCL decoders at high signal-to-noise ratio (SNR) values. Note that in each considered scenario, the FER performance of the decoders are identical.
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